Yes. Most links should be hitting the root domain. Sending a lot of links to multiple inner pages is a novice mistake and an easy way to get your domain penalized. The caveat to this is if your domain has a lot of trust and authority already, but I'm willing to bet yours doesn't.

Social is good. You want link diversity. Just keep in mind that there are two problems with a lot of social platforms; first, they're usually ephemeral, i.e. you hit the top of Reddit, or a Pligg bookmarking site, etc., and it's only a matter of time before your link falls off. Second, many social platforms are no-follow, so the link isn't worth going out of your way for.

Dunno man. No one here can tell you the "why" unless they work for Google -- all I can tell you is that I've done dozens of tests on everything from one page sites to micro-niche sites (~5-10 pages) to sites that have thousands/tens of thousands of pages (cloaked autoblogs). Regardless of site type and niche, for domains without prior age and authority, sending a lot of links to inner pages never provided better results than directing a good majority of them at the domain. Using internal linking to pass linkjuice to internal pages.

"social signals" are becoming increasingly relevant

People have been saying this for years. They're not wrong, but if anything, their importance has probably plateaued. I only use them sporadically when ranking sites and generally notice no difference. So again, they can't hurt, but they're not magic.

First question is a muddy question, you want a natural back link profile from a mix of different PR level sites with a mixture of natural anchor tags. A root link against a page link strongly varies on the source and the goals you have. Honestly take what you can get, keep it natural, keep it distributed.

Socials signals means (IMO) G+ and then a dash of twitter/fb/Pinterest/etc. Even though Google is blocked from crawling a good portion of FB, Google isn't dumb, it sees the referral URL if you're running GA.

A root link against a page link strongly varies on the source and the goals you have.

Our goals are essentially to get people to our shopping pages. Im not sure if they could be considered "long tail". They are like <domain>.com/california-cle. Those are the pages that are important for us to rank highly in search results.

Honestly take what you can get, keep it natural, keep it distributed.

The thing is we are about the ask our partners/content-creators to link to us. We have a choice in where they are sent to and that the links are.